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Hydrostatic pressure at lateral directionsAh I think I get it now -- "the same pressure distribution" leading to "the same total force resulting from hydrostatic pressure" is a result of pressure itself not being a vector, but being a scalar quantity.

Hydrostatic pressure at lateral directionsFrom the first link, "The sides are identical in area, and have the same depth distribution, therefore they also have the same pressure distribution, and consequently the same total force resulting from hydrostatic pressure, exerted perpendicular to the plane of the surface of each side." Can you care to elaborate on this? I still do not really understand why the pressure acting on the top face must be equal to the pressure acting on the side, directly below the top face.

Vector Addition — DirectionSo if I wanted to describe a system of forces and wrote $F_1$ + $F_2$ = $F_3$, $F_3$ is in the opposite direction as $F_1$? But then what about $\Sigma F = ma$? with subtraction we'd say they have opposite directions, but then, they don't right?

Vector Addition — Direction@Debangshu, yes but say $F_1$ and $F_2$ have the same direction and magnitude, and $F_3$ had double their magnitude, and in the opposite direction. $(1)$ would hold, and by subtraction $(2)$ seems to be logically correct. But then $(3)$ would also be true based on what I said about $(1)$, which seems to confuse me.

Mar26

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Vector Addition — Direction@Debangshu, I'm aware of that, but what of the case where $F1$ and $F2$ are of the same direction? $(1)$ still holds, no?